Finite Group Databasebeta

← #24985829

Subgroups — #24985829

Order 11008.

410 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 87 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19141627C211yesmaximal, characteristic
2#19136138C211yesmaximal, characteristic
3#19136073C212yesmaximal
4#19132417C212yesmaximal
5C43×#1272C211yesmaximal, characteristic
6C2×#13063323—21no—
7C2×#13063257—22no—
8C2×#13063256—21no—
9C2×#13063249—21no—
10#14582829—21no—
11#14582820—22no—
12#14582797C2212yes—
13#14582784—22no—
14#14582769C2211yescharacteristic
15#14582662—22no—
16#14582654C2211yescharacteristic
17C43×#391C2211yescharacteristic
18C43×#336C2212yes—
19C22×Dic86—21no—
20C22×C43⋊C8—21no—
21#13063323—42no—
22#13063323—42no—
23C2×C4⋊Dic43—21no—
24C2×C4⋊Dic43—22no—
25C2×C4⋊Dic43—21no—
26C2×C4⋊Dic43D412yes—
27C2×C4⋊Dic43D412yes—
28C2×Dic43⋊C4—22no—
29C2×Dic43⋊C4—22no—
30C2×C4×Dic43—21no—
31#13063257—44no—
32#13063256—42no—
33#13063249—42no—
34C43⋊#95—21no—
35C43⋊#95—22no—
36C43⋊#95—22no—
37C22×Q8×C43D411yescharacteristic
38C22×C8×C43—22no—
39C2×C4⋊C4×C43D411yescharacteristic
40C2×C42×C43C2311yescharacteristic
41#95×C43—22no—
42C2×Q8×C43—21no—
43C2×Q8×C43—41no—
44C2×Q8×C43—41no—
45C2×Q8×C43SD1612yes—
46C22×C4×C43—21no—
47C22×C4×C43—21no—
48C22×C4×C43C2×D411yescharacteristic
49C22×C4×C43C2×D412yes—
50C22×Dic43—22no—
51C22×Dic43—22no—
52C22×Dic43—41no—
53C2×Dic86—42no—
54C2×Dic86—81no—
55C2×Dic86—81no—
56C2×C8×C43—24no—
57C2×C8×C43—42no—
58C2×C8×C43—42no—
59C4⋊C4×C43—41no—
60C42×C43—41no—
61C4⋊Dic43—22no—
62C4⋊Dic43—42no—
63C4⋊Dic43—41no—
64C4⋊Dic43—41no—
65C4⋊Dic43—42no—
66C4⋊Dic43—42no—
67C4⋊Dic43—81no—
68C4⋊Dic43SD1614yes—
69Dic43⋊C4—44no—
70Dic43⋊C4—42no—
71Dic43⋊C4—42no—
72C4×Dic43—42no—
73C2×C43⋊C8—22no—
74C2×C43⋊C8—41no—
75C2×C43⋊C8—41no—
76C23×C43#12011yescharacteristic
77Q8×C43—42no—
78Q8×C43—81no—
79C2×C4×C43—21no—
80C2×C4×C43—22no—
81C2×C4×C43—21no—
82C2×C4×C43—22no—
83C2×C4×C43—22no—
84C2×C4×C43—41no—
85C2×C4×C43—41no—
86C2×C4×C43—41no—
87C2×C4×C43—42no—
88C2×C4×C43C2×SD1612yes—
89C2×C4×C43C2×SD1611yescharacteristic
90C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
91C2×C4×C43#13712yes—
92C2×Dic43—24no—
93C2×Dic43—42no—
94C2×Dic43—42no—
95C2×Dic43—42no—
96C2×Dic43—42no—
97C2×Dic43—42no—
98C2×Dic43—82no—
99C2×Dic43—81no—
100Dic86—84no—
101C8×C43—44no—
102C43⋊C8—42no—
103#7817—431nomaximal, Sylow
104C22×C43#44812yes—
105C22×C43#45011yescharacteristic
106C22×C43#45311yescharacteristic
107C22×C43#45612yes—
108C22×C43#45811yescharacteristic
109C4×C43—22no—
110C4×C43—22no—
111C4×C43—21no—
112C4×C43—21no—
113C4×C43—42no—
114C4×C43—81no—
115Dic43—44no—
116Dic43—82no—
117Dic43—161no—
118#2734—431no—
119#2096—431no—
120#2084—432no—
121#1272D4311yescharacteristic
122#1271—432no—
123C2×C43#161112yes—
124C2×C43#161311yescharacteristic
125C2×C43#162311yescharacteristic
126C2×C43#165112yes—
127C2×C43#166011yescharacteristic
128C2×C4⋊Q8—861no—
129C2×#106—862no—
130C2×#106—861no—
131C2×#103—861no—
132#398—861no—
133#395—862no—
134#391C2×D4311yescharacteristic
135#389—432no—
136#387—862no—
137#384—431no—
138#340—862no—
139#336—431no—
140#336C2×D4312yes—
141C43#781711yescharacteristic, complemented, Sylow
142C22×Q8—861no—
143C22×Q8D17211yescharacteristic
144C22×C8—22no—
145C22×C8—861no—
146C4⋊Q8—1722no—
147C4⋊Q8—1722no—
148C2×C4⋊C4—432no—
149C2×C4⋊C4—432no—
150C2×C4⋊C4—861no—
151C2×C4⋊C4—862no—
152C2×C4⋊C4—862no—
153C2×C4⋊C4—861no—
154C2×C4⋊C4—862no—
155C2×C4⋊C4D17211yescharacteristic
156C2×C42—861no—
157C2×C42C22×D4311yescharacteristic
158#106—1722no—
159#106—1724no—
160#103—1722no—
161#95—22no—
162#95—861no—
163#95—862no—
164#95—862no—
165C2×Q8—21no—
166C2×Q8—41no—
167C2×Q8—41no—
168C2×Q8—3441no—
169C2×Q8—3441no—
170C2×Q8—1722no—
171C2×Q8#1062187312yes—
172C22×C4—21no—
173C22×C4—21no—
174C22×C4—862no—
175C22×C4—862no—
176C22×C4—1721no—
177C22×C4C2×D17211yescharacteristic
178C22×C4D4×D4312yes—
179C2×C8—24no—
180C2×C8—42no—
181C2×C8—42no—
182C2×C8—862no—
183C2×C8—1721no—
184C2×C8—1721no—
185C4⋊C4—41no—
186C4⋊C4—434no—
187C4⋊C4—862no—
188C4⋊C4—3441no—
189C4⋊C4—1721no—
190C4⋊C4—1721no—
191C4⋊C4—1722no—
192C4⋊C4—1724no—
193C4⋊C4—1722no—
194C4⋊C4—1722no—
195C4⋊C4—1722no—
196C4⋊C4—1722no—
197C42—41no—
198C42—1722no—
199C23#1306329511yescharacteristic
200Q8—42no—
201Q8—81no—
202Q8—3444no—
203C2×C4—21no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—21no—
207C2×C4—22no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—42no—
212C2×C4—864no—
213C2×C4—3441no—
214C2×C4—3442no—
215C2×C4—1722no—
216C2×C4—1722no—
217C2×C4—1722no—
218C2×C4—1722no—
219C2×C4—1722no—
220C2×C4SD16×D4312yes—
221C2×C4C2×#1062187311yescharacteristic
222C2×C4#1306335311yescharacteristic
223C2×C4#1306335712yes—
224C8—44no—
225C8—1722no—
226C22#1458303912yes—
227C22#1458305211yescharacteristic
228C22#1458306911yescharacteristic
229C22#1458308312yes—
230C22#1458309011yescharacteristic
231C4—22no—
232C4—22no—
233C4—21no—
234C4—21no—
235C4—42no—
236C4—81no—
237C4—3442no—
238C4—1724no—
239C4—6881no—
240C2#1913360412yes—
241C2#1913361711yescharacteristic
242C2#1913367411yescharacteristic
243C2#1913386112yes—
244C2#1913390711yescharacteristic
subgroupG/H
centerC23#13063295
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1272C2
socle, prime radicalC23×C43#120
hypercenter#1272D43
hypocenterC43#7817
LCSG ▷ C2×C42×C43 ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1272

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
141. C43#7817semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#191416272
#191361382
#191360732
#191324172
C43×#12722
#781743